Solve 1-5x/6-2leq3-x/24

$$\frac { 1 - 5 x } { 6 } - 2 \leq \frac { 3 - x } { 24 }$$

Solve for x

$$x\geq -\frac{47}{19}$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 6,24. Since 24 is positive, the inequality direction remains the same.

$$4\left(1-5x\right)-48\leq 3-x$$

Use the distributive property to multiply 4 by 1-5x.

$$4-20x-48\leq 3-x$$

Subtract 48 from 4 to get -44.

$$-44-20x\leq 3-x$$

Add x to both sides.

$$-44-20x+x\leq 3$$

Combine -20x and x to get -19x.

$$-44-19x\leq 3$$

Add 44 to both sides.

$$-19x\leq 3+44$$

Add 3 and 44 to get 47.

$$-19x\leq 47$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$x\geq -\frac{47}{19}$$